Question

 A population has mean 75 and standard deviation 12.

c) Random samples of size 121 are taken. Find the mean and standard deviation of

the sample mean.

Answer 1

X ~ N ( µ = 75 , σ = 12 )

Part a)

Mean of the sample mean µ_X̅ = µ = 75

Standard deviation of sample mean σ_X̅$=$σ/$\sqrt{(n)}$ $=$ 12$/$ $\sqrt{121}$

$=$ 1.0909

Partb;

Mean of the sample mean µ_X̅ = µ = 75

Standard deviation of sample mean σ_X̅ = σ$/$ $\sqrt{(n)}$ $=$ 12$/$ $\sqrt{400}$

=0.6